This paper is concerned with the moving horizon estimation problem for networked systems over relay channels. The relay channel under consideration is a wireless communication channel with a so-called relay node. Under the effects of relay node, the signal transmission between the plant and estimator is determined by a combination of three communication processes, namely the sensor-to-estimator, the sensor-to-relay and the relay-to-estimator communication processes. In order to characterize the impact of such kind of relay-channel-based communication, a three-terminal relay model is employed to describe the signal transmission behaviors between the plant and the estimator. Three Bernoulli-distributed white sequences are adopted to model the packet losses occurring in the communication processes. A full information estimation strategy is firstly developed in the sense of maximum a posteriori according to the system dynamics and transmission behaviors. Then, a moving horizon estimator is designed based on the derived full information estimation strategy. Furthermore, the solution of the proposed moving horizon estimation strategy is achieved by using the completing-the-square approach and, subsequently, sufficient conditions are derived to guarantee the mean-square ultimate boundedness of the resultant error dynamics of the state estimation. Two simulation examples are given to demonstrate the effectiveness of our developed estimation scheme.

本文研究了中继信道上网络系统的移动水平估计问题。所考虑的中继信道是具有所谓的中继节点的无线通信信道。在中继节点的作用下，被控对象与估计器之间的信号传输由三个通信过程的组合决定，即传感器到估计器、传感器到继电器和中继到估计器的通信过程。为了表征这种基于中继信道的通信的影响，采用三端中继模型来描述设备和估计器之间的信号传输行为。采用三个伯努利分布的白色序列对丢包进行建模发生在沟通过程中。根据系统动力学和传输行为，首先在最大后验意义上开发了全信息估计策略。然后，基于推导的全信息估计策略设计了移动水平估计器。此外，所提出的移动水平估计策略的解决方案是通过使用完成平方方法来实现的，随后，导出了充分的条件来保证状态估计的合成误差动力学的均方最终有界性。给出了两个模拟示例来证明我们开发的估计方案的有效性。